The gears of low-speed have low frequency characteristics of faults. The frequency of fault is covered by background noise, and the fault signals are difficult to be accurately demodulated and extracted. In this paper, a parameter optimization-based variational algorithm decomposition (POVMD) and a cyclic autocorrelation function (CAF) diagnosis method are proposed to solve this problem. First, the original signal is decomposed by POVMD, and the cosine similarity is used to select the sensitive intrinsic mode function (IMF). Secondly, the spectrum of the sensitive components of the cyclic autocorrelation function is calculated to gain the slice of the spectrum of the autocorrelation function. Finally, Teager energy operator (TEO) is used to extract the fault feature frequency in the spectrum of instantaneous amplitude of the slice. This method is compared with related methods. The feature extraction effect is more significant. Simulation signal and experimental data analysis verify the validity and reliability of the proposed method.